One-dimensional topological semilattices

One Dimensional Topological Lattices

The lattice theoretic terminology used in this paper is consistent with Birkhoff [2]. The topological terms can be found in [5] or [8] with the following exceptions. If X and Y are sets, X\Y denotes the relative compliment of Y with respect to X. If A is a subset of a topological space then A*, A"and FiA)=A*\A° denote the topological closure, interior and boundary of A. The symbol 0 denotes the...

One{dimensional Topological Dynamics

A Faster One-Dimensional Topological Compaction Algorithm

We consider the problem of one-dimensional topological com-paction with jog insertions. Combining both geometric and graph the-oretic approaches we present a faster and simpler algorithm, improving over previous results. The compaction algorithm takes as input a sketch consisting of a set F of features and a set W of wires, and minimizes the horizontal width of the sketch while maintaining its ...

Topological dynamics of one-dimensional cellular automata

1 Glossary Almost equicontinuous CA has an equicontinuous configuration. Attractor: omega-limit of a clopen invariant set. Blocking word interrupts information flow. Closing CA: distinct asymptotic configurations have distinct images. Column subshift: columns in space-time diagrams. Cross section: one-sided inverse map. ∗Université de Nice Sophia Antipolis, Département d’Informatique, Parc Valr...

Upper Semilattices of Finite-dimensional Gauges

This is a brief overview of some applications of the ideas of abstract convexity to the upper semilattices of gauges in finite dimensions.